juniorbenitez00
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The mass of a regulation tennis ball is 57 g. The ball is in contact with the tennis racket for 30 ms. The ball was served at 73.14 m/s. If the opponent returned the serve with a speed of 55 m/s, what force did he exert on the ball, assuming only horizontal motion?

Respuesta :

grujan50

Answer:

Correct answer:  F₂ = 104.5 N

Explanation:

Given:

m = 57 g = 57 · 10⁻³ kg

Δt = 30 ms = 30 · 10 ⁻³ seconds

V₁ = 73.14 m/s   service speed

V₂ = 55 m/s  returned speed

M = m · V  Momentum or Impulse

You forgot to indicate what time the ball contact when returning.

We will assume that the time is the same Δt = 30 ms = 30 10 ⁻³ seconds.

The formula for calculating force is according to Newton's second law is:

F = ΔM / Δt = m · ΔV / Δt

Force during service is:

F₁ = 57 · 10⁻³ · 73.14 / 30 · 10 ⁻³ = 138.97 N

F₁ = 138.97 N

Returned force:

F₂ =  57 · 10⁻³ · 55 / 30 · 10 ⁻³ = 104.5 N

F₂ =  104.5 N

God is with you!!!

hamzaahmeds

This question involves the concepts of Newton's Second Law of Motion, Momentum, and Force.

The force exerted on the ball is "- 243.5 N".

According to Newton's Second Law of Motion, the force applied to a body is equal to the rate of change of its momentum.

[tex]F = \frac{\Delta P}{t}\\\\F = \frac{m(v_f-v_i)}{t}\\\\[/tex]

where,

F = Force = ?

m = mass = 57 g = 0.057 kg

vf = final speed = -55 m/s (negative sign due to change in direction)

vi = 73.14 m/s

t = 30 ms = 0.03 s

Therefore,

[tex]F = \frac{(0.057\ kg)(- 55\ ms/ - 73.14\ m/s)}{0.03\ s}[/tex]

F = -243.5 N

A negative sign shows reaction force.

Learn more about Newton's Second Law of Motion here:

https://brainly.com/question/13447525?referrer=searchResults

The attached picture shows Newton's Second Law of Motion.

Ver imagen hamzaahmeds

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